The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A349274 Decimal expansion of the arc length of the logarithmic spiral related to a golden triangle with a unit base length. 1
 4, 9, 2, 5, 1, 7, 5, 4, 3, 9, 4, 7, 8, 0, 5, 8, 8, 3, 7, 1, 9, 3, 1, 7, 6, 0, 4, 6, 8, 1, 3, 5, 6, 5, 6, 7, 4, 2, 2, 4, 5, 7, 0, 1, 9, 2, 8, 4, 0, 6, 9, 5, 2, 2, 2, 1, 5, 2, 0, 5, 8, 0, 2, 2, 0, 9, 4, 6, 3, 2, 5, 2, 4, 4, 3, 4, 6, 5, 2, 2, 6, 3, 3, 9, 0, 1, 5, 4, 3, 1, 5, 2, 0, 7, 8, 4, 4, 6, 8, 9, 5, 8, 3, 4, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The spiral starts at the triangle's apex (the vertex opposite to the base) and converges to the pole (the accumulation point). REFERENCES H. E. Huntley, The Divine Proportion: A Study in Mathematical Beauty, New York: Dover Publications Inc., 1970, pp. 170-176. Mario Livio, The Golden Ratio: The Story of Phi, The World's Most Astonishing Number, New York: Broadway Books, 2002, p. 119. LINKS Table of n, a(n) for n=1..105. Amiram Eldar, Golden triangle and logarithmic spiral - illustration. Hiroaki Kimpara, Logarithmic Spirals based on the Golden Ratio, Golden Square Ratio, Silver Ratio, and Silver Square Ratio, 2011. Eric Weisstein's World of Mathematics, Golden Triangle. Eric Weisstein's World of Mathematics, Logarithmic Spiral. Wikipedia, Golden triangle (mathematics). Wikipedia, Logarithmic spiral. FORMULA Equals sqrt((17 + 7*sqrt(5))/22) * sqrt(1 + b^2)/b, where b = 5*log(phi)/(3*Pi), and phi = (1+sqrt(5))/2 is the golden ratio (A001622). EXAMPLE 4.92517543947805883719317604681356567422457019284069... MATHEMATICA b = 5 * Log[GoldenRatio]/(3*Pi); RealDigits[Sqrt[(17 + 7*Sqrt[5])/22] * Sqrt[1 + b^2]/b, 10, 100][[1]] CROSSREFS Cf. A001622, A296794. Sequence in context: A125575 A254159 A199725 * A021071 A197146 A021207 Adjacent sequences: A349271 A349272 A349273 * A349275 A349276 A349277 KEYWORD nonn,cons AUTHOR Amiram Eldar, Nov 12 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 18 01:35 EDT 2024. Contains 375995 sequences. (Running on oeis4.)